/*===========================================================================
 
 Copyright (C) 2002-2012 Yves Renard.
 
 This file is a part of GETFEM++
 
 Getfem++  is  free software;  you  can  redistribute  it  and/or modify it
 under  the  terms  of the  GNU  Lesser General Public License as published
 by  the  Free Software Foundation;  either version 3 of the License,  or
 (at your option) any later version along with the GCC Runtime Library
 Exception either version 3.1 or (at your option) any later version.
 This program  is  distributed  in  the  hope  that it will be useful,  but
 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
 or  FITNESS  FOR  A PARTICULAR PURPOSE.  See the GNU Lesser General Public
 License and GCC Runtime Library Exception for more details.
 You  should  have received a copy of the GNU Lesser General Public License
 along  with  this program;  if not, write to the Free Software Foundation,
 Inc., 51 Franklin St, Fifth Floor, Boston, MA  02110-1301, USA.
 
===========================================================================*/
#include "getfem/bgeot_poly.h"

using std::endl; using std::cout; using std::cerr;
using std::ends; using std::cin;


std::string horner_print(bgeot::short_type degree, bgeot::power_index &mi,
			 bgeot::short_type k, bgeot::short_type de) {
  char s[1024];
  const char *xyz = "xyzabcdefghijklmnop";
  if (k == 0) {
    sprintf(s, "P[%d]", int(mi.global_index()));
    return s;
  } else {
    std::string str;
    //T v = (*(it+k-1)), res = T(0);
    for (mi[k-1] = bgeot::short_type(degree-de);
	 mi[k-1] != bgeot::short_type(-1); (mi[k-1])--) {
      //res = horner(mi, k-1, de + mi[k-1], it) + v * res;
      if (str.size())
	sprintf(s, "%s + %c*(%s)",
		horner_print(degree, mi,bgeot::short_type(k-1),bgeot::short_type(de+mi[k-1])).c_str(), xyz[k-1],
		str.c_str());
      else 
	sprintf(s, "%s", horner_print(degree, mi,bgeot::short_type(k-1),bgeot::short_type(de+mi[k-1])).c_str());
      str = s;
    }
    mi[k-1] = 0;
    return str;
  }
}


void dump_poly_eval() {
  for (bgeot::short_type dim = 1; dim <= 3; ++dim) {
    cout << "case " << dim << ": {\n";
    for (unsigned k=0; k < dim; ++k) {
      cout << "T " << "xyzZ"[k] << " = it[" << k << "];\n";
    }
    for (bgeot::short_type dg=2; dg <= 6; ++dg) {
      cout << "  if (deg == " << dg << ") ";
      bgeot::power_index mi(dim);
      cout << "    return " << horner_print(dg, mi, dim, 0) << ";\n";
    }
    cout << "} break;\n";
  }
}

int main(void)
{
  try {

    bgeot::base_poly W, Z; W[0] = 1.0;
    Z[0] = 2.0;
    cout << "rd = " << W.real_degree() << endl;
    cout << "W = " << W << endl;
    W.direct_product(Z);
    cout << "W = " << W << endl;

    bgeot::base_poly P(2,2), Q(2,2);
    P[2] = 1.0;
    Q[3] = 2.0;
    cout << "Le nombre de monomes de P est " << P.size() << endl;
    cout << "P = " << P << endl;
    cout << "Q = " << Q << endl;
    cout << "P + Q = " << P + Q << endl;
    cout << "P * 2.0 * Q = " << P * 2.0 * Q << endl;
    bgeot::base_poly R = P * Q;
    cout << "Le nombre de monomes de R est " << R.size() << endl;
    cout << "Le degre de R est " << R.degree() << endl;
    P.direct_product(Q);
    cout << "Produit direct de P et Q : " << P << endl;
    
    Z.direct_product(P);
    cout << "Produit direct de P et Z : " << Z << endl;    

    P = bgeot::base_poly(3,1,1);
    P *= 3.0; P *= bgeot::base_poly(3,1,0);
    P += bgeot::base_poly(3,1,1);
    P *= bgeot::base_poly(3,1,2);
    P += bgeot::base_poly(3,1,0);
    cout << "P = " << P << " : degree=" << P.degree() << endl;
    
    
    bgeot::opt_long_scalar_type tab[3];
    tab[0] = 1.0; tab[1] = 2.0; tab[2] = -1.0;
    
    cout << "P(1.0, 2.0) = " << P.eval(&(tab[0])) << endl;

    for (bgeot::short_type dg=0; dg <= 6; ++dg) {
      for (bgeot::short_type dim=0; dim <= 3; ++dim) {
	bgeot::base_poly PP(dim, dg);
	for (unsigned i=0; i < PP.size(); ++i) 
	  PP[i] = bgeot::opt_long_scalar_type(rand())
	    / bgeot::opt_long_scalar_type(RAND_MAX);
	std::vector<bgeot::opt_long_scalar_type> X(dim); 
	for (unsigned i=0; i < dim; ++i) X[i] = 
	  bgeot::opt_long_scalar_type(rand())
	  / bgeot::opt_long_scalar_type(RAND_MAX);
	bgeot::opt_long_scalar_type a = PP.eval(X.begin());
	bgeot::power_index mi(dim);
	bgeot::opt_long_scalar_type b = PP.horner(mi,dim,0,X.begin());

	cout << "[d=" << dim << ", dg=" << PP.degree() 
	  //<< ", P=" << PP << " -> " 
	     << a << " == " << b 
	     << "?\n";
	assert(gmm::abs(a-b) < 1e-14);
	
	//cout << "Horner: " << PP.horner_print(mi,dim,0) << "\n";
      }
    }
    cout << "\n--------------------------------------------------------\n";
    dump_poly_eval();
    cout << "\n--------------------------------------------------------\n";

    
    Q = P;
    P *= Q;
    cout << "PP = " << P << "\n";
    P.derivative(0);
    cout << "PP.derivative(0)=" << P << "\n";

    bgeot::power_index p(3);
    for (int i=0; i < 20; ++i, ++p) {
      cout << "i=" << i << ", p=";
      for (unsigned k=0; k < p.size(); ++k) cout << p[k] << " ";
      cout << "degree=" << p.degree() << ", global_index(p)="
	   << p.global_index() << "\n";      
    }

    bgeot::base_poly S(1,2); S[0] = -2; S[1] = 3; S[2] = 1;
    cout << "P=" << P << ", S=" << S << " \n";
    cout << "P(S,x)=" << bgeot::poly_substitute_var(P,S,0) << "\n";
    bgeot::opt_long_scalar_type t0 = gmm::uclock_sec();
    std::vector<bgeot::opt_long_scalar_type> v(3);
    for (unsigned i=0; i < 100000; ++i) {
      for (unsigned k=0; k < v.size(); ++k)
	v[k] =  bgeot::opt_long_scalar_type(rand())
	  / bgeot::opt_long_scalar_type(RAND_MAX);
      P.eval(v.begin());
    }
    cout << "poly eval : " << gmm::uclock_sec() - t0 << "sec \n";
    bgeot::base_poly QQ(P); QQ.derivative(1); QQ.derivative(2);
    cout << "QQ=" << QQ << "\n";
    for (unsigned i=0; i < 100000; ++i) {
      QQ.eval(v.begin());
    }
    cout << "poly eval : " << gmm::uclock_sec() - t0 << "sec \n";

    t0 = gmm::uclock_sec();
    bgeot::opt_long_scalar_type z=0;
    for (unsigned i=0; i < 100000; ++i) {
      bgeot::base_poly P2(P);
      for (bgeot::short_type k=0; k < P.dim(); ++k) { 
        P2.derivative(k); z += P2[0];
      }
    }
    cout << "poly derivative : " << gmm::uclock_sec() - t0 << "sec\n";

    bgeot::base_poly P2;
    std::stringstream ss; ss << P;
    P2 = bgeot::read_base_poly(P.dim(), ss);
    cout << "P=" << P << "\nread_base_poly=" << P2 << "\n";
    assert(P == P2);
  }
  GMM_STANDARD_CATCH_ERROR;

  return 0;
}
